Summary

In this innovative new Linear Algebra text, award-winning educator David Poole covers vectors and vector geometry first to enable students to visualize the mathematics while they are doing matrix operations. Rather than merely doing the calculations with no understanding of the mathematics, students will be able to visualize and understand the meaning of the calculations. By seeing the mathematics and understanding the underlying geometry, students will develop mathematical maturity and learn to think abstractly.

Table of Contents

Preface

xi

To the Instructor

xix

To the Student

xxv

Vectors

1

(56)

Introduction: The Racetrack Game

1

(2)

The Geometry and Algebra of Vectors

3

(13)

Length and Angle: The Dot Product

16

(16)

Exploration: Vectors and Geometry

30

(2)

Lines and Planes

32

(16)

Exploration: The Cross Product

46

(2)

Code Vectors and Modular Arithmetic

48

(9)

Systems of Linear Equations

57

(74)

Introduction: Triviality

57

(1)

Introduction to Systems of Linear Equations

58

(9)

Exploration: Lies My Computer Told Me

65

(2)

Direct Methods for Solving Linear Systems

67

(22)

Exploration: Partial Pivoting

85

(1)

Exploration: Counting Operations---An Introduction to the Analysis of Algorithms